Which, while interesting, doesn't change the original point: that GPS satellites do not have to take general or special relativity into account in order to function correctly. They remain accurate regardless of time dilation factors, because only a time difference BETWEEN ANY TWO SATELLITES would introduce calculation errors, and that difference is both 1) very very small and 2) eliminated manually on a regular basis.
I suppose specialized clocks that synch with GPS satellites probably do (I've never seen one, so I'll take your word for it) but since those clocks aren't triangulating your exact location from a GPS signal it's kind of a moot point.
